Corollary 3.21.
Every pointed object \(X \in T_*\) is \((-1)\)-connected.
Proof
A basepoint \(x\colon * \to X\) determines a section of the map \(X \to *\), which by Lemma 2.38 implies that \(X \to *\) is an effective epimorphism, hence \((-1)\)-connected.